7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Numerical analysis of time-evolution starting from equilibrium states ofelectrically non-neutral two-fluid plasmas by 2D3V PIC simulation
1

Y. Nakajima1, M. Sengupta2, H. Himura1, A. Sanpei1
Department of Electronics, Kyoto Institute of Technology
2
Lawrence Livermore National Laboratory
e-mail (speaker): d2822003@edu.kit.ac.jp

Two-fluid plasma models, which describe ion-electron
plasmas as two individual fluids, play a role in detailingthe dynamics and deriving novel equilibria of the plasma.
In addition, current enthusiastic efforts to verify
two-fluid effects in plasmas such as transport of relative
canonical helicity[1] or turbulences in tokamak edge
region[2], require electrically non-neutrality of plasmas.
To investigate how electrically non-neutrality affects theconfinement of the plasmas, one way would be to findstable equilibrium states in geometrically simple
configurations. Therefore, as one of the simple
configurations, we have been considering an infinitely
long cylindrical electrically non-neutral plasma andderiving the equilibria numerically. However, its stability
has not been analyzed. In this presentation, we show
numerical analysis of time-evolution starting fromequilibrium states of counter-differential rigid-rotation
equilibria of electrically non-neutral two-fluid plasma[3]by 2D3V PIC code[4]. In the equilibria, ion (i+) andelectron (e-) plasmas with finite temperatures are
confined cylindrically by a uniform magnetic field B
exhibit corresponding rigid rotations around the plasma
axis with different angular velocities ωi and ωe, which is
attributed to the contribution from the diamagnetic driftof the i+ and e- plasma owing to its finite pressures.
While the equilibrium state has been experimentallyexplored[5,6], its stability has also been investigatedthrough numerical studies. To analyze the stability, thePIC code calculates its time-evolution of the particle
distributions or density profiles of i+ and e- plasmas

initially in the equilibria. The PIC simulation calculates
the spatial and temporal evolution of the ion and electron
superparticles. As an initial condition of the calculation,
106 ion and e- superparticles are placed each in thedensity profile of the equilibrium state. The positions andvelocities of the superparticles are then calculated every
10 pico-seconds, which is sufficiently shorter than thecyclotron period of e- and i+. Figure 1 shows ion velocity
field obtained from the distribution of superparticles byusing cloud-in-cell method. This indicates that there isazimuthal ion flow in the plasma. This corresponds to thefact that the counter-differential rigid-rotation is driven
by a diamagnetic drift. Furthermore, as shown in Figure
2, an examination of the energy in this case reveals thatthe kinetic energy oscillates in time while the totalenergy itself grows slowly. These results are discussed.

Figure 1: Velocity field of ions 40us after the startof the PIC simulation. B is into the plane of thepaper. X and y are normalized by 𝑎 = 0.5, which
is a radius of confinement wall. The ion velocity
𝑣𝑖 is also normalized by a thermal velocity of ion
𝑣𝑡ℎ = 4.9 × 103 m/s.

Figure 2: Time-evolution of kinetic and totalenergy starting from equilibrium states ofelectrically non-neutral two-fluid plasmas. Theenergies are normalized by initial uniform
temperature of ion plasma 𝑇𝑖0 = 2 eV. The time isnormalized by ion cyclotron period of ion 𝜏𝑖 = 3.6μs.

References[1] J. Linden, et al., Phys. Rev. Lett. 121.3,035001(2018).
[2] B. Zhu, et al., Physics of Plasmas 24.5, 055903(2017).
[3] Y. Nakajima, et al., J. Plasma Phys. 87.4, 905870415(2021).
[4] M. Sengupta, et al., J. Applied Phys. 129. 22, 223302(2021).
[5] Y. Nakajima, et al., AIP Advances 12, 045015 (2022).
[6] T. Okada, et al., Physics Letters A, 460, 128617(2023).